Tangents and Normals

The subnormal at any point on the curve $y^n=ax$ is a constant. Then the value of $n$ is

Find the abscissa of the point on the curve $3y = 6x - 5x^3$, the normal at which passes through origin is

The abscissa of the point on the curve $3y=6x-5x^3,$ the normal at which passes through origin is

The slope of the tangent to the curve $y=\frac{2x+1}{3-x},x\ne 3$ at the point $\left(2,5\right)$ is equal to

The curve $y=x^{1/5}$ at $\left(0,0\right)$ has

The point on the curve $y^2=x$, where the tangent makes an angle of $45°$ with $x$ axis is,

Index numbers are used in:

If with a rise of $10\%$ in prices the wages are increased by $20\%$ the real wage increases by:

_____play a very important role in the construction of index numbers:

The criteria for an ideal estimator are:
 

In_____distribution, Mean = Variance:

An unbiased coin is tossed 3 times, the expected value of the number of heads is:

$P\left(A_1\right)=3/8;P\left(A_2\right)=2/3;P\left(A_1\cap A_2\right)=1/4$ then $A_1$ and $A_2$ will be:

There are 6 positive and 8 negative numbers. Four numbers are selected at random without replacement and multiplied. Find the probability that the product is positive:

When $\mathrm{r}=1$, all the points in a scatter diagram would lie:

The SD of $\mathrm{X}$ is known to be 10 then the $\mathrm{SD}$ of $50+5 \mathrm{X}$ is:

If every observation is increased by 5 then:

Co-efficient of QD is equal to_____:

The equation of the curve which passes through the point $\left(1,2\right)$ and has the slope $3\mathrm{x}-4$ at any point $\left(\mathrm{x}, \mathrm{y}\right)$ is:

${\int }_1^e\frac{e^x\left(x{\log }_{e}x+1\right)}{x}dx$: